Functional Approach to Nonlinear Models of Water Flow in Soils

This book is a work of applied mathematics focusing on the functional study of the nonlinear boundary value problems relating to water flow in porous media. As far as revealed by the literature, a systematic study of these models within the above mentioned framework has not been done and the book has been written with the belief that the abstract theory may be sometimes easier and richer in consequences for applications than standard classical approaches are. The volume deals with diffusion type models and emphasizes the mathematical treatment of their nonlinear aspects. A unifying functional approach to different boundary value problems modelling the water movement in porous media is presented, and the high degree of generality and abstraction, kept however within reasonable limits, is rewarded by the richness of the results obtained in this way.

From the mathematical point of view the results obtained can be considered as general results in the theory of nonlinear parabolic equations. Although water flow in soils was the principal exemplification for the functional treatment, the techniques used within the book and the results obtained here turn out useful for studying other appropriate problems arising in general in the movement of fluids in porous media, in the heat theory, phase transitions, biology, chemistry or engineering.